On numerical relativistic hydrodynamics and barotropic equations of state

TL;DR

This paper discusses modifications to the characteristic formulation of relativistic hydrodynamics for barotropic flows, addressing singularities and proposing solutions to improve numerical stability and accuracy.

Contribution

It introduces a simple renormalization method to remove singularities in eigenvectors for barotropic equations of state in relativistic hydrodynamics.

Findings

Singularity in eigenvectors can be avoided by renormalization.

Alternative strategies for barotropic flows are discussed.

Method improves the robustness of relativistic hydrodynamic simulations.

Abstract

The characteristic formulation of the relativistic hydrodynamic equations (Donat et al 1998 J. Comput. Phys. 146 58), which has been implemented in many relativistic hydro-codes that make use of Godunov-type methods, has to be slightly modified in the case of evolving barotropic flows. For a barotropic equation of state, a removable singularity appears in one of the eigenvectors. The singularity can be avoided by means of a simple renormalization which makes the system of eigenvectors well defined and complete. An alternative strategy for the particular case of barotropic flows is discussed.